# How do you find the remainder for (x^3+6x^2-4x+2)div(x+1)?

Nov 2, 2016

Use the Remainder Theorem . The remainder is 11

#### Explanation:

The Remainder Theorm states that:

Given a polynomial, $p \left(x\right)$, the remainder, $r \left(a\right)$, of the division, $p \left(x\right) \div \left(x - a\right)$, is equal to the polynomial evaluated at a:

$r \left(a\right) = p \left(a\right)$

$\left(x + 1\right) = \left(x - - 1\right)$, therefore, $a = - 1$

Evaluate the polynomial at -1:

${\left(- 1\right)}^{3} + 6 {\left(- 1\right)}^{2} - 4 \left(- 1\right) + 2 = 11$

The remainder is 11.